Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#2150 ⋊ C2 |
| Sylow | C5 ⋊ D4×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C23×D5 |
| commutator, socle | C22×C5 | C23×C8 |
| Fitting | C5×#2150 | C2 |
| prime radical | C22×D20 | C8 |
| cosocle | C2×C5×C8 | C24 |
| hypercenter | #2150 | D5 |
| hypocenter | C5 | D4×M32 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C8 ◁ #2150 | |
734 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,c^2=f,f^2=g,g^2=h,b^a=be,d^a=dh,i^b=i^4,d^c=dh,i^c=i^4212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322780);